FINAL EXAM REVIEW Chapter 5 Key Concepts

Chapter 5 Vocabulary parallelogram ► opposite sides ► opposite angles ► diagonals rectanglerhombussquaretrapezoid

Defn. of a Parallelogram A quadrilateral with both pairs of opposite sides parallel In ABCD, AB DC and AD BC A B CD

Theorem Opposite sides of a parallelogram are congruent.

Theorem Opposite angles of a parallelogram are congruent.

Theorem Diagonals of a parallelogram bisect each other.

Theorem One pair of opp. sides both // and = ~ Parallelogram

The Five Ways to Show a Quadrilateral is a Parallelogram 2) Both pairs of opp. sides = ~ 3) One pair of opp. sides both // and = ~ 4) Both pairs of opp. ‘s = ~ 7 5) Diagonals bisect each other 1) Defn. of

Theorem If 2 lines are parallel, then all points on one line are equidistant from the other line. AB l m CD AC = BD

Theorem If 3 parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. A B C X Y Z If AB = BC then XY = YZ

Theorem A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side. YZ X M N If M is the midpoint of XY then N is the midpoint of XZ

Theorem A segment that joins the midpoints of 2 sides of a triangle; 1. is parallel to the third side. 2. is half as long as the third side. YZ X M N 1.MN YZ 2.MN = ½YZ

Theorem: The diagonals of a rectangle are congruent

Theorem: The diagonals of a rhombus are perpendicular.

Theorem: Each diagonal of a rhombus bisects two angles of the rhombus.

Theorem: The midpoint of the hypotenuse of a right triangle is equidistant from all three vertices..

Theorem: If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.

Theorem: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

Trapezoid (Defn.) A quadrilateral with exactly one pair of parallel sides. leg base

IsoscelesTrapezoid (Defn.) A trapezoid with congruent legs.

Theorem Base angles of an isosceles trapezoid are congruent.

Theorem The median of a trapezoid: 1. is parallel to the bases. 2. has a length equal to the average of the base lengths. median AB CD XY XY = ½(AB + CD)

Homework ► Chapter 5 Review WS